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The longtime evolution of mean field magnetohydrodynamics
An epidemiology model that includes a leaky vaccine with a general waning function
1.  Department of Mathematics and Statistics, University of Victoria, Victoria B.C., Canada V8W 3P4, Canada, Canada 
2.  Department of Mathematics, Pomona College, Claremont, CA 917116348, United States 
3.  Programa de Matemáticas Aplicadas y Computación, Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, San Bartolo Atepehuacan, D.F. 07730, Mexico 
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[2] 
Linda J. S. Allen, P. van den Driessche. Stochastic epidemic models with a backward bifurcation. Mathematical Biosciences & Engineering, 2006, 3 (3) : 445458. doi: 10.3934/mbe.2006.3.445 
[3] 
Benjamin H. Singer, Denise E. Kirschner. Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfection. Mathematical Biosciences & Engineering, 2004, 1 (1) : 8193. doi: 10.3934/mbe.2004.1.81 
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Muntaser Safan, Klaus Dietz. On the eradicability of infections with partially protective vaccination in models with backward bifurcation. Mathematical Biosciences & Engineering, 2009, 6 (2) : 395407. doi: 10.3934/mbe.2009.6.395 
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Tomás Caraballo, Renato Colucci, Luca Guerrini. Bifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case study. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 26392655. doi: 10.3934/dcdsb.2018268 
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Qianqian Cui, Zhipeng Qiu, Ling Ding. An SIR epidemic model with vaccination in a patchy environment. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 11411157. doi: 10.3934/mbe.2017059 
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Urszula Foryś, Jan Poleszczuk. A delaydifferential equation model of HIV related cancerimmune system dynamics. Mathematical Biosciences & Engineering, 2011, 8 (2) : 627641. doi: 10.3934/mbe.2011.8.627 
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Shujing Gao, Dehui Xie, Lansun Chen. Pulse vaccination strategy in a delayed sir epidemic model with vertical transmission. Discrete & Continuous Dynamical Systems  B, 2007, 7 (1) : 7786. doi: 10.3934/dcdsb.2007.7.77 
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Geni Gupur, XueZhi Li. Global stability of an agestructured SIRS epidemic model with vaccination. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 643652. doi: 10.3934/dcdsb.2004.4.643 
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Aili Wang, Yanni Xiao, Robert A. Cheke. Global dynamics of a piecewise epidemic model with switching vaccination strategy. Discrete & Continuous Dynamical Systems  B, 2014, 19 (9) : 29152940. doi: 10.3934/dcdsb.2014.19.2915 
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Zhigui Lin, Yinan Zhao, Peng Zhou. The infected frontier in an SEIR epidemic model with infinite delay. Discrete & Continuous Dynamical Systems  B, 2013, 18 (9) : 23552376. doi: 10.3934/dcdsb.2013.18.2355 
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Sumei Li, Yicang Zhou. Backward bifurcation of an HTLVI model with immune response. Discrete & Continuous Dynamical Systems  B, 2016, 21 (3) : 863881. doi: 10.3934/dcdsb.2016.21.863 
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Ying Hu, Shanjian Tang. Switching game of backward stochastic differential equations and associated system of obliquely reflected backward stochastic differential equations. Discrete & Continuous Dynamical Systems  A, 2015, 35 (11) : 54475465. doi: 10.3934/dcds.2015.35.5447 
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Xiao Wang, Zhaohui Yang, Xiongwei Liu. Periodic and almost periodic oscillations in a delay differential equation system with timevarying coefficients. Discrete & Continuous Dynamical Systems  A, 2017, 37 (12) : 61236138. doi: 10.3934/dcds.2017263 
[15] 
Eugen Stumpf. On a delay differential equation arising from a carfollowing model: Wavefront solutions with constantspeed and their stability. Discrete & Continuous Dynamical Systems  B, 2017, 22 (9) : 33173340. doi: 10.3934/dcdsb.2017139 
[16] 
Eugenii Shustin. Exponential decay of oscillations in a multidimensional delay differential system. Conference Publications, 2003, 2003 (Special) : 809816. doi: 10.3934/proc.2003.2003.809 
[17] 
Fengqi Yi, Eamonn A. Gaffney, Sungrim SeirinLee. The bifurcation analysis of turing pattern formation induced by delay and diffusion in the Schnakenberg system. Discrete & Continuous Dynamical Systems  B, 2017, 22 (2) : 647668. doi: 10.3934/dcdsb.2017031 
[18] 
C. Connell McCluskey. Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence. Mathematical Biosciences & Engineering, 2010, 7 (4) : 837850. doi: 10.3934/mbe.2010.7.837 
[19] 
Masaki Sekiguchi, Emiko Ishiwata, Yukihiko Nakata. Dynamics of an ultradiscrete SIR epidemic model with time delay. Mathematical Biosciences & Engineering, 2018, 15 (3) : 653666. doi: 10.3934/mbe.2018029 
[20] 
Lin Zhao, ZhiCheng Wang, Liang Zhang. Threshold dynamics of a time periodic and two–group epidemic model with distributed delay. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 15351563. doi: 10.3934/mbe.2017080 
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